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3 years ago

Sarah is training for a bike race . She rides her bike 5 3/4 miles in 45 minutes.what is Sarah's rate in mile per hour ?

Mathematics

1 answer:

poizon [28]3 years ago

3 0

Answer:

7.6667 miles per hour

Step-by-step explanation:

Since the question is asking for her rate in Miles per hour. We want to convert the given time (minutes) to hours. 45 minutes is simply 3/4 of an hour, or 0.75 hours.

Now that we have how many miles she biked and how many hours it took, we simply divide the two values.

By converting 5 and 3/4 into a single fraction it would be 23/4, so we would divide 23/4 by 0.75 hours to get the final answer of 7.6667 miles per hour.

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3 years ago

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sp2606 [1]

Answer:

$y = -\frac{3}{2} x + 4$

Step-by-step explanation:

First, let us find the gradient of AB:

Gradient of AB = $\frac{-1-3}{-1-5}$

= $\frac{2}{3}$

We also need to know that The product of gradients which are perpendicular to each other is -1. Using this idea, we can find the gradient of the perpendicular bisector:

(Gradient of perpendicular bisector)( $\frac{2}{3}$ ) = -1

Gradient of perpendicular bisector = $-\frac{3}{2}$

Now, we need to know at which coordinates the perpendicular bisector intersects AB. A perpendicular bisector bisects a line to two equal parts. Hence the coordinates of the intersection point is the midpoint of AB. Thus,

Coordinates of intersection = ( $\frac{-1 + 5}{2}$ , $\frac{-1 + 3}{2}$ )

= ( 2, 1 )

Now, we can construct our equation. The equation of a line can be formed using the formula $(y - y_{1}) = m(x - x_{1})$ where $m$ is the gradient and the line passes through $(x_{1} , y_{1} )$ . Hence by substituting the values, we get: